To Understand what is an Irrational number we have to understand what is a rational number? Rational number are those numbers which can be expressed in the form of numerator / denominator. Every rational numbers can be expressed as decimal form or in non- terminating repeating decimal form..
Definition of Irrational number: Irrational numbers are those numbers which cannot be expressed in the form of numerator / denominator. all non- terminating non- recurring decimals are irrational number.
What is a irrational number
According to definition of Irrational numbers : Any number that cannot be expressed in the form of p/q , where p , q are integers , q>0 , p and q have no common factor (except 1) is called an irrational number.
What are irrational number
- Negative of an irrational number is an irrational number.
- The sum of a rational number and an irrational number is considered as an irrational number.
- The product of a non-zero rational number and an irrational number is found to be irrational in nature.
- The sum, difference , product , and quotient of two irrational numbers need not to be an irrational number because the sum of the irrational numbers √3 and -√3 is 0 which is a rational number, whereas the sum of irrational number √2 and √5 is an irrational number
- The difference of an irrational numbers √2 and -√2 is zero which is a rational number but √5 and √ 6 difference is irrational number.
- The product of √18 and √ 2 is 6, which is a rational number and √7 and √6 is √42 which is irrational.
- The quotient of irrational number √12 and √ 3 is 2 , which is a rational number and √12 and √4 is √3 is irrational number.
What is an irrational number
A number is an irrational number , if it has non-terminating an non repeating decimal representation.
- Let us take some Irrational numbers examples 0.12112111211112………., 0.30003000030000003…………….. cannot be expressed in the form of p/q.
- The decimal representation of √2=1.414215…………………. is neither terminating nor repeating so , it is an irrational number.
